Leeds, which missed out on a return to the Premier League after losing in the Championship play-offs, was handed a trip to Salford in the week commencing 13 August during Friday's (AEST) draw that took place in a store of UK chain Morrisons.
Salford is in the English Football League for the first time after their rapid rise, after a takeover by members of Manchester United's famed 'Class of 92', which helped fuel a series of promotions.
The club's part-owner Gary Neville enjoyed Salford's draw, writing on Twitter: "Welcome back into my life Leeds United. Not seen you for 15 years."
Huddersfield Town is at home to Lincoln City after its relegation from the Premier League, while AFC Wimbledon has been handed a crunch clash against MK Dons.
Cardiff City and Fulham, the two other clubs to drop into the Championship, will enter at the second-round stage with Premier League sides who are not in Europe.